Sets, Relations & Functions · JEE Main previous year questions

387 questions asked across 19 exam years, newest first

Year-wise papers Topic-wise questions

Practise this topic

2021 30 questions

Q122021 · 1 Sept 2021 · Shift 2
The range of the function, $f (x) = lo g_{5} (3 + cos (\frac{3 π}{4} + x) + cos (\frac{π}{4} + x) + cos (\frac{π}{4} - x) - cos (\frac{3 π}{4} - x))$ is :
1. A. $(0, 5)$
2. B. $[- 2, 2]$
3. C. $[\frac{1}{5}, 5]$
4. D. $[0, 2]$
Show answer
Answer: D
Q142021 · 1 Sept 2021 · Shift 2
The function f(x), that satisfies the condition $f (x) = x + \int_{0}^{π /2} sin x cos y f (y) d y$ , is :
1. A. $x + \frac{2}{3} (π - 2) sin x$
2. B. $x + (π + 2) sin x$
3. C. $x + \frac{π}{2} sin x$
4. D. $x + (π - 2) sin x$
Show answer
Answer: D
Q32021 · 26 Aug 2021 · Shift 2
The local maximum value of the function $f (x) = (\frac{2}{x})^{x^{2}}$ , $x > 0$ , is
1. A. $(2 e)^{\frac{1}{e}}$
2. B. $(\frac{4}{e})^{\frac{e}{4}}$
3. C. $(e)^{\frac{2}{e}}$
4. D.1
Show answer
Answer: C
Q62021 · 26 Aug 2021 · Shift 2
The domain of the function $cosec^{- 1} (\frac{1 + x}{x})$ is :
1. A. $(- 1, - \frac{1}{2}] \cup (0, \infty)$
2. B. $[- \frac{1}{2}, 0) \cup [1, \infty)$
3. C. $(- \frac{1}{2}, \infty) - {0}$
4. D. $[- \frac{1}{2}, \infty) - {0}$
Show answer
Answer: D
Q222021 · 26 Aug 2021 · Shift 2· Numerical answer
Let a and b respectively be the points of local maximum and local minimum of the function $f (x) = 2 x^{3} - 3 x^{2} - 12 x$ . If A is the total area of the region bounded by $y = f (x)$ , the x-axis and the lines $x = a$ and $x = b$ , then 4A is equal to ________.
Show answer
Answer: 114
Q122021 · 27 Jul 2021 · Shift 2
Let $f : [0, \infty) \to [0, 3]$ be a function defined by $f (x) = {max {sin t : 0 \leq t \leq x}, 2 + cos x, 0 \leq x \leq π x > π$ Then which of the following is true?
1. A.f is continuous everywhere but not differentiable exactly at one point in $(0, \infty)$
2. B.f is differentiable everywhere in $(0, \infty)$
3. C.f is not continuous exactly at two points in $(0, \infty)$
4. D.f is continuous everywhere but not differentiable exactly at two points in $(0, \infty)$
Show answer
Answer: B
Q132021 · 27 Jul 2021 · Shift 2
Let N be the set of natural numbers and a relation R on N be defined by $R = {(x, y) \in N \times N : x^{3} - 3 x^{2} y - x y^{2} + 3 y^{3} = 0}$ . Then the relation R is :
1. A.symmetric but neither reflexive nor transitive
2. B.reflexive but neither symmetric nor transitive
3. C.reflexive and symmetric, but not transitive
4. D.an equivalence relation
Show answer
Answer: B
Q262021 · 27 Jul 2021 · Shift 2· Numerical answer
Let $A = {n \in N ∣ n^{2} \leq n + 10, 000}$ , $B = {3 k + 1 ∣ k \in N}$ and $C = {2 k ∣ k \in N}$ , then the sum of all the elements of the set $A \cap (B - C)$ is equal to ____.
Show answer
Answer: 832
Q82021 · 25 Jul 2021 · Shift 1
The area (in sq. units) of the region, given by the set ${(x, y) \in R \times R ∣ x \geq 0, 2 x^{2} \leq y \leq 4 - 2 x}$ is :
1. A. $\frac{8}{3}$
2. B. $\frac{17}{3}$
3. C. $\frac{13}{3}$
4. D. $\frac{7}{3}$
Show answer
Answer: D
Q282021 · 25 Jul 2021 · Shift 1· Numerical answer
Let $S = {n \in N (01 i 0)^{n} (a c b d) = (a c b d) \forall a, b, c, d \in R}$ , where $i = - 1$ . Then the number of 2-digit numbers in the set S is ____.
Show answer
Answer: 11
Q302021 · 25 Jul 2021 · Shift 1· Numerical answer
Let $M = {A = (a c b d) : a, b, c, d \in {\pm 3, \pm 2, \pm 1, 0}}$ . Define f : M $\to$ Z, as f(A) = det(A), for all $A \in M$ , where z is set of all integers. Then the number of $A \in M$ such that f(A) = 15 is equal to ____.
Show answer
Answer: 16
Q132021 · 25 Jul 2021 · Shift 2
Consider function f : A $\to$ B and g : B $\to$ C (A, B, C $\subseteq$ R) such that $(g o f)^{- 1}$ exists, then :
1. A.f and g both are one-one
2. B.f and g both are onto
3. C.f is one-one and g is onto
4. D.f is onto and g is one-one
Show answer
Answer: C
Q22021 · 22 Jul 2021 · Shift 2
Let $f : R \to R$ be defined as $f (x) = {- \frac{4}{3} x^{3} + 2 x^{2} + 3 x, 3 x e^{x}, x > 0 x \leq 0 .$ Then f is increasing function in the interval
1. A. $(- \frac{1}{2}, 2)$
2. B. $(0, 2)$
3. C. $(- 1, \frac{3}{2})$
4. D. $(- 3, - 1)$
Show answer
Answer: C
Q122021 · 22 Jul 2021 · Shift 2
If the domain of the function $f (x) = \frac{c o s ^{- 1} x ^{2} - x + 1}{s i n ^{- 1} ( \frac{2 x - 1}{2} )}$ is the interval $(α, β]$ , then $α + β$ is equal to :
1. A. $\frac{3}{2}$
2. B. $2$
3. C. $\frac{1}{2}$
4. D. $1$
Show answer
Answer: A
Q212021 · 22 Jul 2021 · Shift 2· Numerical answer
Let $A = {0, 1, 2, 3, 4, 5, 6, 7}$ . Then the number of bijective functions $f : A \to A$ such that $f (1) + f (2) = 3 - f (3)$ is equal to
Show answer
Answer: 720
Q252021 · 22 Jul 2021 · Shift 2· Numerical answer
The sum of all the elements in the set ${n \in {1, 2, \dots, 100} ∣ H.C.F. of n and 2040 is 1}$ is equal to ________.
Show answer
Answer: 1251
Q302021 · 22 Jul 2021 · Shift 2· Numerical answer
The number of elements in the set ${n \in {1, 2, 3, \dots, 100} ∣ (11)^{n} > (10)^{n} + (9)^{n}}$ is ________.
Show answer
Answer: 96
Q72021 · 20 Jul 2021 · Shift 1
Let [ x ] denote the greatest integer $\leq x$ , where $x \in R$ . If the domain of the real valued function $f (x) = \frac{∣ [ x ] ∣ - 2}{∣ [ x ] ∣ - 3}$ is $(- \infty, a) \cup [b, c) \cup [4, \infty)$ , $a < b < c$ , then the value of a + b + c is :
1. A.8
2. B.1
3. C. $- 2$
4. D. $- 3$
Show answer
Answer: C
Q122021 · 20 Jul 2021 · Shift 1
Let 'a' be a real number such that the function $f (x) = a x^{2} + 6 x - 15, x \in R$ is increasing in $(- \infty, \frac{3}{4})$ and decreasing in $(\frac{3}{4}, \infty)$ . Then the function $g (x) = a x^{2} - 6 x + 15, x \in R$ has a :
1. A.local maximum at $x = - \frac{3}{4}$
2. B.local minimum at $x = - \frac{3}{4}$
3. C.local maximum at $x = \frac{3}{4}$
4. D.local minimum at $x = \frac{3}{4}$
Show answer
Answer: A
Q102021 · 18 Mar 2021 · Shift 1
The real valued function $f (x) = \frac{cosec ^{- 1} x}{x - [ x ]}$ , where $[x]$ denotes the greatest integer less than or equal to $x$ , is defined for all $x$ belonging to :
1. A.all real except integers
2. B.all non-integers except the interval $[- 1, 1]$
3. C.all integers except $0, - 1, 1$
4. D.all real except the interval $[- 1, 1]$
Show answer
Answer: B
Q112021 · 18 Mar 2021 · Shift 1
If the functions are defined as $f (x) = x$ and $g (x) = 1 - x$ , then what is the common domain of the following functions : $f + g, f - g, f / g, g / f, g - f$ where $(f \pm g) (x) = f (x) \pm g (x), (f / g) x = \frac{f ( x )}{g ( x )}$
1. A. $0 \leq x \leq 1$
2. B. $0 \leq x < 1$
3. C. $0 < x < 1$
4. D. $0 < x \leq 1$
Show answer
Answer: C
Q42021 · 16 Mar 2021 · Shift 1
The number of elements in the set ${x \in R : (∣ x ∣ - 3) ∣ x + 4∣ = 6}$ is equal to :
1. A.4
2. B.2
3. C.3
4. D.1
Show answer
Answer: B
Q92021 · 16 Mar 2021 · Shift 1
Let the functions $f : R \to R$ and $g : R \to R$ be defined as : $f (x) = {x + 2, x^{2}, x < 0 x \geq 0$ and $g (x) = {x^{3}, 3 x - 2, x < 1 x \geq 1$ Then, the number of points in $R$ where $(f \circ g) (x)$ is NOT differentiable is equal to :
1. A.0
2. B.3
3. C.1
4. D.2
Show answer
Answer: C
Q112021 · 16 Mar 2021 · Shift 1
The range of $a \in R$ for which the function $f (x) = (4 a - 3) (x + lo g_{e} 5) + 2 (a - 7) cot (\frac{x}{2}) sin^{2} (\frac{x}{2})$ , $x \neq = 2 nπ, n \in N$ has critical points, is :
1. A. $[1, \infty)$
2. B. $(- 3, 1)$
3. C. $[- \frac{4}{3}, 2]$
4. D. $(- \infty, - 1]$
Show answer
Answer: C
Q62021 · 26 Feb 2021 · Shift 1
Let R = {(P, Q) | P and Q are at the same distance from the origin} be a relation, then the equivalence class of $(1, - 1)$ is the set :
1. A. $S = {(x, y) ∣ x^{2} + y^{2} = 2}$
2. B. $S = {(x, y) ∣ x^{2} + y^{2} = 2}$
3. C. $S = {(x, y) ∣ x^{2} + y^{2} = 1}$
4. D. $S = {(x, y) ∣ x^{2} + y^{2} = 4}$
Show answer
Answer: B